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Marginal Rate of Technical Substitution
The following production table gives estimates of the maximum amounts of output possible with different combinations of two input factors, X and Y. (Assume that these are just illustrative points on a spectrum of continuous input combinations.)
Units of Y Used
Estimated Output per Day
5
210
305
360
421
470
4
188
272
324
376
3
162
234
282
2
130
1
94
Do the two inputs exhibit the characteristics of constant, increasing, or decreasing marginal rates of technical substitution? How do you know? Assuming that output sells for $3 per unit, complete the following tables: Assume that the quantity of X is fixed at 2 units. If output sells for $3 and the cost of Y is $120 per day, how many units of Y will be employed? Assume that the company is currently producing 162 units of output per day using 1 unit of X and 3 units of Y. The daily cost per unit of X is $120 and that of Y is also $120. Would you recommend a change in the present input combination? Why or why not? What is the nature of the returns to scale for this production system if the optimal input combination requires that X = Y?
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